Answer :
A person with moment of inertia i is spinning at an angular velocity ω. At some point in time he moves his arm position such that his moment of inertia changes to 2i. the rotational kinetic energy k of the person after the change, in terms of his initial rotational kinetic energy is 1/4 .
The moment of inertia of a rigid body, also referred to as the mass moment of inertia, angular mass, second moment of mass, or more precisely, rotational inertia, is a property that establishes the torque required for the desired angular acceleration about a rotational axis, much like mass establishes the force required for the desired acceleration. The amount of torque required to modify the body's rate of rotation depends on the mass distribution of the body and the axis selected. For example, larger moments require more torque.
The moment of inertia for a point mass is equal to the mass squared by the perpendicular distance from the axis of rotation. This is an extensive (additive) property.
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